Abstract: Number theory is founded on the basic properties of integers and prime numbers. But its study these days is increasingly leading us to the far reaches of some of the most diverse and powerful areas of mathematics. Nowhere is this more apparent than in the Langlands program, which represents a profound unifying force for mathematics.

We shall try to introduce the Langlands program through the theory of L-functions. These are infinite series that look like the famous Riemann zeta function, except that they have nontrivial coefficients. The information that goes into the coefficients is in fact very interesting, and gives an elegant way of organizing fundamental data from number theory, representation theory and algebraic geometry. The Langlands program postulates deep relationships among different L-functions, and hence also the data in their coefficients.

We shall discuss these matters, and explain how they are part of the theory of automorphic forms. We shall then describe the trace formula, which has led to important results in the classification of automorphic representations. If time permits, we shall also say something about Beyond Endoscopy, a proposal by Langlands for attacking the central conjecture of the subject known as the Principle of Functoriality.

The Department of Mathematics at the University of Virginia invites applications for several postdoctoral positions, including Whyburn Instructorships, to begin the fall semester of 2017. These positions carry a three-year appointment. Preference will be given to candidates who have received their Ph.D. within the last three years. Applicants must be on track to receive a Ph.D. in the relevant field by May 2017 and must hold a Ph.D. at the time of appointment. Applicants must present evidence of outstanding accomplishments and promise in both research and teaching. All candidates whose research interests complement the strengths of the department's current faculty will be considered. Information about the department may be found at www.math.virginia.edu.

Review of applications will begin on November 15, 2016; however, the positions will remain open until filled.

To apply candidates must submit a Candidate Profile through Jobs@UVa (https://jobs.virginia.edu), search on posting number 0619358 and electronically attach the following: a cover letter of interest describing research agenda and teaching experience, a curriculum vitae, and contact information for four references.

In addition, please submit the following required documents electronically through www.MathJobs.org: A cover letter, an AMS Standard Cover Sheet, a curriculum vitae, a publication list, a description of research, and a statement about teaching interests and experience. The applicant must also have at least four letters of recommendation submitted, of which one must support the applicant's effectiveness as a teacher.

The University will perform background checks on all new faculty hires prior to making a final offer of employment.

The University of Virginia is an equal opportunity and affirmative action employer. Women, minorities, veterans, and persons with disabilities are encouraged to apply.

Assistant Professor in Mathematics

UNIVERSITY OF VIRGINIA

Department of Mathematics

The Department of Mathematics at the University of Virginia, Charlottesville, VA, invites applications for a tenure-track Assistant Professor full time position. Applicants must present evidence of outstanding accomplishments and promise in both research and teaching. We seek candidates dedicated to our mission and passionate about teaching in a world class institution.

In addition to developing external funding to support research endeavors, candidates will be expected to teach at the graduate and undergraduate levels and provide service to the University, Department and professional organizations. The appointment is anticipated to begin with the fall term of 2017, with an anticipated start date of July 25, 2017. Applicants must be on track to receive a Ph.D. in the relevant field by May 2017 and must hold a PhD at the time of appointment. Preference will be given to applicants whose research program is in Algebraic Geometry or Analysis, but all candidates whose research interests complement the strengths of the department's current faculty will be considered.

To apply candidates must submit a Candidate Profile through Jobs@UVa (https://jobs.virginia.edu), search on posting number 0619419 and electronically attach the following: a cover letter of interest describing research agenda and teaching experience, a curriculum vitae, and contact information for four references.

Review of applications will begin November 1, 2016; however, the positions will remain open until filled.

In addition, please submit the following required documents electronically through www.MathJobs.org: A cover letter, an AMS Standard Cover Sheet, a curriculum vitae, a publication list, a description of research, and a statement about teaching interests and experience. The applicant must also have at least four letters of recommendation submitted, of which one must support the applicant's effectiveness as a teacher.

The University will perform background checks on all new faculty hires prior to making a final offer of employment.

The University of Virginia is an equal opportunity/affirmative action employer. Women, minorities, veterans, and persons with disabilities are encouraged to apply.

Lecturer/Instructor

UNIVERSITY OF VIRGINIA

Department of Mathematics

The University of Virginia Department of Mathematics seeks applications to fill non-tenure track Lecturer and Instructor positions for the Fall 2016 and/or Spring 2017 semester. Subject areas of particular need include: Calculus and other undergraduate Mathematics courses. Compensation will take the form of wages. A terminal degree is expected but not required. Candidates must have a strong commitment to teaching. Applications will be considered immediately.

To apply, please complete a Candidate Profile online through Jobs@UVa (https://jobs.virginia.edu), and search Posting #0618834 and electronically attach the following: a current CV, cover letter, and complete contact information for three professional references.

Eugene C. Paige, Jr. 1929-2016

Thursday, June 30, 2016

Xiang Wan Receives Outstanding Graduate Teaching Assistant Award

Tuesday, May 31, 2016

We are happy to announce that the department of mathematics' Outstanding Graduate Teaching Assistant award for 2015-16 has been awarded to Xiang Wan. As winner of the departmental award, Xiang was nominated to compete for a University-wide award, and was selected as one of the top 15 of a very accomplished group of teachers. He was presented with a Jefferson Cup in honor of his achievement.

The department also recognizes two graduate teaching assistants with Honorable Mentions for our teaching award: they are Peter Bonventre and Jonathan Simone. All three of these outstanding GTAs will receive recognition and a cash prize at this year’s graduation ceremony.

Congratulations to Xiang, Peter, and Jon!

Final Exercises Ceremony for the College and Graduate School of Arts and Sciences

Saturday, May 21, 2016

In 2016, the Final Exercises ceremony for the College and Graduate School of Arts & Sciences will be on Saturday, May 21 with the department graduation ceremonies following that afternoon. The fair-, inclement-, and severe-weather ceremony sites for Mathematics will be:

*Please note that Gilmer Hall Room 130 is a Remote Viewing Location for Finals on the Lawn. We anticipate that the remote viewing will conclude prior to 12 p.m.

Under the severe-weather plan, ALL degree candidates (undergraduate and graduate) will participate in the ceremony at John Paul Jones Arena. Each graduating student will receive six guest seating tickets for the Lawn. Since we cannot accommodate as many people in the arena compared to the Lawn, graduates will be restricted to three guests if the ceremony is moved inside. Tickets are required for all guests either on the Lawn or at the arena. Guests without tickets can watch a live broadcast of the ceremony at one of the remote viewing locations across Grounds.

Complimentary parking will be available at Scott Stadium and at John Paul Jones Arena with shuttle bus service to Central Grounds. Buses will load at the entrance of the Student Activities Building (located in the Scott Stadium west parking lot) and near the west entrance of the arena. Return shuttles to these lots will run continuously from Central Grounds throughout Saturday afternoon. Parking is also available in the Emmet/Ivy parking garage ($5 per vehicle), which is about a 10 minute walk to the Lawn (no shuttle service).

Karen Smith February 29th - March 2nd, 2016

Tuesday, May 3, 2016

Karen Smith (University of Michigan)

Algebra, Geometry and Analysis over Finite Fields

Lecture 1: Monday, February 29th, 2016
Time: 5:00PM-6:00PM
Location: Clark 108
Abstract: In this lecture, we review how Noether's introduction of the concept of an abstract ring changed the course of mathematics in the twentieth century by enabling us to apply the methods of "reduction modulo p" to solve problems in algebraic geometry. Specifically, I'll discuss how understanding solutions to polynomials over finite fields can help understand the geometry of geometric objects (called varieties) defined by real or complex polynomials. Miraculously, rings of characteristic p have some very special properties that can be powerful tools in analyzing them, often replacing tools like integration for real manifolds.

Lecture 2: Tuesday, March 1st, 2016
Time: 5:00PM-6:00PM
Location: Clark 108
Abstract: In the second lecture, we review Hironaka's famous theorem on the resolution of singularities of a complex algebraic variety. We show this theorem can help us understand and measure the singularities of complex varieties. Amazingly, it turns out that the only algebraic characterization of a geometric condition called "rational singularities" involves reduction to characteristic p. Specifically, we will see how algebraic tools such as Frobenius splitting impact different areas of math, including the minimal model program for complex algebraic varieties and cluster algebras in combinatorics/representation theory.

Lecture 3: Wednesday, March 2nd, 2016
Time: 3:30-4:30
Location: Physics 203
Abstract: In the final lecture, we discuss a numerical invariant of singularities called the analytic index of singularities, which is defined by the convergence of a certain integral. Amazingly, this invariant turns out to have a prime characteristic description as well, as the limit, over all primes p, of another invariant called the F-pure threshold. The study of these F-pure thresholds leads to some very interesting and mysterious fractal like behavior.

Congratulations to Award Recipient Jiahua Liu

Friday, April 22, 2016

We are proud to report that Jiahua Liu has been selected to receive the International Studies Office Award for international undergraduate student academic excellence. He will be honored at the awards ceremony for graduating international students and their families this May. Congratulations, Jiahua Liu!

2016 Putnam Award Winners

Friday, April 22, 2016

The 2016 Putnam Award Winners include Sifan Ye, Juan Velasco, and Arun Kannan. Congratulations to all three on this impressive accomplishment!

2016 E.J. McShane Prize in Mathematics winner - Alexander Grieser

Friday, April 22, 2016

The award announcements at the Gordon E. Keller Mathematics Majors Dinner revealed this year's recipient of the E.J. McShane Prize in Mathematics to be Alexander Grieser. Congratualtions to Alexander on this accomplishment!

Ben Webster receives Cory Family Teaching Award

Thursday, April 21, 2016

Congratulations to Ben Webster! He is one of two 2016 recipients of the prestigious Cory Family Teaching Awards, and joins David Sherman (2013) among the award recipients from the Mathematics department. The Cory Family Teaching Awards are "designed to reward and incentivize excellence in teaching among junior faculty." Since 2013 and continuing through 2017, two junior faculty members are chosen as recipients and honored at Fall Convocation. Each recipient is awarded $25,000 thanks to the generosity of Mr. and Mrs. Charles R. Cory. Well done, Ben!